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Sparse Representation for Brain Signal Processing: A tutorial on methods and applications

机译：脑信号处理的稀疏表示：方法和应用指南

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In many cases, observed brain signals can be assumed as the linear mixtures of unknown brain sources/components. It is the task of blind source separation (BSS) to find the sources. However, the number of brain sources is generally larger than the number of mixtures, which leads to an underdetermined model with infinite solutions. Under the reasonable assumption that brain sources are sparse within a domain, e.g., in the spatial, time, or time-frequency domain, we may obtain the sources through sparse representation. As explained in this article, several other typical problems, e.g., feature selection in brain signal processing, can also be formulated as the underdetermined linear model and solved by sparse representation. This article first reviews the probabilistic results of the equivalence between two important sparse solutions?the 0-norm and 1-norm solutions. In sparse representation-based brain component analysis including blind separation of brain sources and electroencephalogram (EEG) inverse imaging, the equivalence is related to the recoverability of the sources. This article also focuses on the applications of sparse representation in brain signal processing, including components extraction, BSS and EEG inverse imaging, feature selection, and classification. Based on functional magnetic resonance imaging (fMRI) and EEG data, the corresponding methods and experimental results are reviewed.
机译：在许多情况下，可以将观察到的脑信号假定为未知脑源/成分的线性混合物。查找来源是盲源分离（BSS）的任务。但是，脑源的数量通常大于混合物的数量，这导致具有无限解的不确定模型。在合理的假设下，脑源在一个域内（例如在空间，时间或时频域内）是稀疏的，我们可以通过稀疏表示来获得这些源。如本文所述，其他一些典型问题（例如脑信号处理中的特征选择）也可以公式化为欠定线性模型，并通过稀疏表示来解决。本文首先回顾两个重要的稀疏解（0范数和1范数解）之间的等价概率结果。在基于稀疏表示的脑成分分析（包括脑源的盲分离和脑电图（EEG）反向成像）中，等效性与源的可恢复性有关。本文还将重点介绍稀疏表示在脑信号处理中的应用，包括成分提取，BSS和EEG逆成像，特征选择和分类。基于功能磁共振成像（fMRI）和脑电图数据，综述了相应的方法和实验结果。

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    《IEEE Signal Processing Magazine》 |2014年第3期|96-106|共11页
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